Lubricating oils have been used in the past in internal combustion engines, gearboxes and other mechanical devices to promote smoother functioning. Internal combustion engine lubricating oils (engine oils), in particular, must exhibit a high level of performance under the high-performance, high-output and harsh operating conditions of internal combustion engines. Various additives such as anti-wear agents, metal cleaning agents, non-ash powders and antioxidants are therefore added to conventional engine oils to meet such performance demands. (See Patent documents 1-3, for example.) The fuel efficiency performance required of lubricating oils has continued to increase in recent years, and this has led to application of various high-viscosity-index base oils or friction modifiers (see Patent document 4, for example).